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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
From 50 students:
37 passed Math, 24 Physics, 43 Chemistry.
At most 19 passed Math & Physics,
at most 29 passed Math & Chemistry,
at most 20 passed Physics & Chemistry.
Intersection of all 3 is $x$.
Find maximum possible value of $x$.
Solution
Use: $M + P + C - (MP + MC + PC) + x \le 50$ Substitute maximum overlaps:
$37 + 24 + 43 - (19 + 29 + 20) + x \le 50$
Compute:
$104 - 68 + x \le 50$
$36 + x \le 50$
$x \le 14$
But each pair overlap already includes $x$, so consistency check:
Maximum possible $x = \min(19, 29, 20) = 19$
No — limited by total count equation → 14.
But must satisfy all pair limits:
If $x=14$:
MP = 19 → remaining just 5
MC = 29 → remaining 15
PC = 20 → remaining 6
All non-negative.
Thus x = 14 possible → but not in options.
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